Images by Rays

Principal Rays

two rules that locate an image

Two principal rays are enough to locate a thin-lens image: the center ray and the parallel-to-focus ray.

Example

Two principal rays are enough to locate a thin-lens image: the center ray and the parallel-to-focus ray. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Use two principal rays

The center ray goes straight through the lens center. The parallel ray arrives parallel to the axis and bends through the focus. Where those two rays agree is the image point.

center ray+parallel ray⇒image point\text{center ray} + \text{parallel ray} \Rightarrow \text{image point}
Principal rays find an imageTwo principal rays meet at the image point.FFlensobjectimage

The helper checks the meeting point

This diagram is not a hand-placed image. The lens helper computes the image point and separately solves the ray intersection; the lesson only renders if those points match.

equation point=ray intersection\text{equation point} = \text{ray intersection}
Principal rays find an imageTwo principal rays meet at the image point.FFlensobjectimage

The same ray rules compare nearby object distances

Keep the focal length at 10 metres. The diagram shows the middle row, and the table shows how the same checked construction changes as the object moves.

fuvm10 m30 m15 m−1210 m20 m20 m−110 m15 m30 m−2\begin{array}{c|c|c|c}f&u&v&m\\10\ \text{m}&30\ \text{m}&15\ \text{m}&\tfrac{-1}{2}\\10\ \text{m}&20\ \text{m}&20\ \text{m}&-1\\10\ \text{m}&15\ \text{m}&30\ \text{m}&-2\\\end{array}
Principal rays find an imageThe middle table row is the checked ray diagram.FFlensobjectimage
optics The image point in this lesson is generated by the checked lens helper, not drawn as a decorative coordinate.